Pith Number

pith:4YLQP5LS

pith:2012:4YLQP5LSQ5GFEKV4FSVKZ2BMXI

not attested not anchored not stored refs pending

The fractional chromatic number of triangle-free subcubic graphs

Daniel Kr\'al', David Ferguson, Tom\'a\v{s} Kaiser

arxiv:1203.1308 v3 · 2012-03-06 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4YLQP5LSQ5GFEKV4FSVKZ2BMXI}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:26:42.884071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e61707f572874c522abc2caaace82cba0c246bb1efe68faabf5723a0047701a2

Aliases

arxiv: 1203.1308 · arxiv_version: 1203.1308v3 · doi: 10.48550/arxiv.1203.1308 · pith_short_12: 4YLQP5LSQ5GF · pith_short_16: 4YLQP5LSQ5GFEKV4 · pith_short_8: 4YLQP5LS

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4YLQP5LSQ5GFEKV4FSVKZ2BMXI \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e61707f572874c522abc2caaace82cba0c246bb1efe68faabf5723a0047701a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98f5ec9a773ea6a4582a9cfa00a1abdd522bcae9fe60c92442329d6d728ac191",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-06T20:34:06Z",
    "title_canon_sha256": "54a0fa0e62724292aca0e617699ae90dd2d656786e10f699cb82103dd465dd66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.1308",
    "kind": "arxiv",
    "version": 3
  }
}